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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 287r

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.73.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 288v); this page is its right half.

The machine reads it as

  1. Resumonus ergo. Aequatio factitia data est: V , . DB . gaV qa 16 a
  2. Aequatio data quadrato quadralica: V IV am V taenY + ap. 0.
  3. a qua sublito secundo termino, Scribemus: 1V4 X + a WB + ae ZW + a51. 50
  4. et reducendo ad cubicam, + + 2t 7 L= 1a 7 27
  5. a
  6. 272
  7. =a5, et opuendo e7 F fiet
  8. fiet aequatio culica talis: 5 + .75 + 2 5 - a X r
  9. et sublato varce termine secunde quae cujus radices ita nultis licaui possunt, ut unam habeat
  10. cum factitia simili terminum communem. De quo postea, nunc teutare operae pretium
  11. duxi facillimam omnium madhinationem, secundo termino non sublato: nimirum,
  12. habemus: V3 + . 8V + 2 a V + qa V + 6 a H 0, aequationem factitiam
  13. et Y. 1V nam V + anV + a e 0. aequationem datam; ponatur V p Ny, tiet
  14. ex aequatione factitia: X Y + 2D A + Y a X + 9a s y + 6a
  15. 0a
  16. ca
  17. rai
  18. divisisque omnibus per N fiet. yt 2Da V3 + 2aa V 9~ a 1 +6a a
  19. ar,
  20. Seo
  21. ox
  22. ON
  23. 93
  24. am, fiet s a . sed parum, hinc, opinor, incris
  25. ponanus jam s en vd fiet NV + 24 ~ V 1 7 2q B - a d et
  26. divisisque omnbus per N, fret: B2 14 a B +
  27. a
  28. ponatur dacta BX + CX r ha, fiet: aequatio factitia ) X - 1VCX 2+ Y S X + C X e) Aequatio factitia. V + 26DD + 26YV
  29. (N) C
  30. + ya
  31. X q
  32. +
  33. a
  34. 40 3
  35. V- 42
  36. N3
  37. (+ . D8 p
  38. Fo Z-ava
  39. oipa 1) Far crm
  40. 0 (1) O (7)
  41. conferenda cum 6V + 8 1V + oan D + n D + 02 p p o
  42. Enit DE Olatemt QB Oam D + Z E tem.d. 1 n + 8 Y Extem 1.
  43. d5i cteg1.
  44. aq. 2. 28
  45. Aeq. 3.
  46. tuea p +07e,
  47. ponatur Q 1) e P, siit ex terminis altims Ay e B - oan + ar cn si o p
  48. vee n e + a + 4r q = ap, fietue: ex terminis quartis: 2V4, +
  49. in quacto termino factitico reperitur n, cujus valor substitut ex quinto, ubu
  50. 0ya e can
  51. et ex hac aequatione crit: Y 2F + a p an
  52. et supra
  53. pa
  54. Oaen + aD
  55. tea +o7n
  56. oa + aron
  57. sed ut rem rectius complectamur considerandum esst
  58. a 8 a= 8r y n ( 207- ’an ex teminis quartis,
  59. et Bxa + 8r 1B a, B f- ap +4r q . Ex teminis stis.
  60. Ergo jangendo 2DZ - an M B F O a + aripes et pro sulsti
  61. tuendo ejus valorem exterminis tertiis, fiet: 1DY n-C anp 4 - 9 a + O B = Oam
  62. ilem jungendo duos alsolulos psius e ontre, fret. 6 an + 18ha + 4
  63. en
  64. rp 10Y +7 20 710 an
  65. +ba + e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 287r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0573?run=74